DOI 10.1140/epje/i2018-11708-6

Topical Review

Eur. Phys. J. E (2018) 41: 97 THE EUROPEANPHYSICAL JOURNAL E

Physico-chemical foundations of particle-laden fluid interfaces�

Armando Maestro1, Eva Santini2, and Eduardo Guzman3,4,a

1 Institut Laue-Langevin, 71 avenue des Martyrs, CS 20156, 38042 Grenoble, Cedex 9, France2 Istituto di Chimica della Materia Condensata e di Tecnologia per l’Energia (ICMATE), U.O.S. Genova-Consiglio Nazionale

delle Ricerche (CNR), Via De Marini 6, 16149 Genova, Italy3 Departamento de Quımica Fısica I, Universidad Complutense de Madrid, Ciudad Universitaria s/n, 28040 Madrid, Spain4 Instituto Pluridisciplinar, Universidad Complutense de Madrid, Paseo Juan XXIII, 1, 28040 Madrid, Spain

Received 31 March 2018 and Received in final form 2 July 2018Published online: 28 August 2018c© EDP Sciences / Societa Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature,2018

Abstract. Particle-laden interfaces are ubiquitous nowadays. The understanding of their properties andstructure is essential for solving different problems of technological and industrial relevance; e.g. stabi-lization of foams, emulsions and thin films. These rely on the response of the interface to mechanicalperturbations. The complex mechanical response appearing in particle-laden interfaces requires deepeningon the understanding of physico-chemical mechanisms underlying the assembly of particles at interfacewhich plays a central role in the distribution of particles at the interface, and in the complex interfacialdynamics appearing in these systems. Therefore, the study of particle-laden interfaces deserves attention toprovide a comprehensive explanation on the complex relaxation mechanisms involved in the stabilizationof fluid interfaces.

1 Introduction

The ubiquity of particle-laden interfaces in both natureand industry has driven, in the last thirty years, the de-velopment of an important research field, which tries tounravel the physico-chemical bases underlying the attach-ment of particles to interfaces, especially fluid ones, i.e.liquid/vapor and liquid/liquid interfaces [1–8]. The exten-sive research focused on the understanding of such sys-tems has raised many questions, associated with the rela-tionship existing between the interactions occurring at thefluid interface (particle-particle, particle-fluids and fluid-fluid interactions), and the structure and properties of theparticle-laden interface [2,6,9–14]. The comprehensive un-derstanding of the aforementioned aspects is mandatoryfor developing processes and products for technologicalpurposes based on the interactions of particles with inter-face [5,8,14–18]. This is a challenge, involving both practi-cal and theoretical efforts, aimed to develop a frameworkproviding a description of complex interplay existing be-tween different physico-chemical properties, e.g. particlewettability, size, shape, surface charge, and chemical na-

� Contribution to the Topical Issue “Flowing Matter, Prob-lems and Applications”, edited by Federico Toschi, IgnacioPagonabarraga Mora, Nuno Araujo, Marcello Sega.

a e-mail: eduardogs@quim.ucm.es

ture of the particles and the interface, with the relativedielectric constant of the phases playing a main role onthe trapping of the particles at fluid interfaces and theinteractions [12].

Among the fields in which particle-laden interfacesplay a key role are included: stabilization of dispersedsystems (foams, emulsions, or thin films), flotation pro-cesses, encapsulation, pharmaceutical formulations, foodtechnology and catalysis [2, 15, 19–24]. However, the im-portant development of such field has also raised differentquestions related to the toxicity for human and environ-mental health of particles, especially those in the nano-size scale [25–29]. Thus, further developments on this fielddeserve a detailed analysis of both the physico-chemicalbases underlying the fabrication processes and the poten-tial risks associated with such processes and materials [30].

The assembly of particles at fluid interfaces leads toa broad range of structures, among which is possible tofind crystalline 2D layers or fractal patterns of particleaggregates [9, 10, 31–34]. It is expected that this varietyof structures affects the mechanical performance of in-terfaces [6, 35], e.g. governing the collapse mechanism ofthe interface through the appearance of buckling, jam-ming, or squeezing-out phenomena upon compression ordensification of the layer [3, 36, 37]. This has been ex-ploited in several applications which rely on the responseof particle-laden interfaces upon dilation and/or shear de-

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formations [7, 8, 38–41]. Furthermore, the understandingof the interfacial relaxation processes of particle layersagainst an external mechanical perturbation plays a cen-tral role for the stabilization of foams and emulsions. Insuch systems, the coating of bubbles or drops by particlelayers provides mechanical stability to the interface, pre-venting destabilization phenomena, such as coalescenceand Ostwald ripening, thus hindering the drainage by agravitational field. This has been exploited from the sem-inal works by Ramsden [42] and Pickering [43] more thanone century ago. Therefore, deepening on the physico-chemical aspects underlying the performance of particle-laden interfaces under dynamic conditions will result inan improvement of their application in the fabrication ofconsumer products [44].

Particle-laden interface can be prepared following twodifferent approaches [1, 45]. The former one considers thedirect self-assembly at the interface of particles from bulkdispersions leading to the formation of the so-called ad-sorbed monolayers [46,47]. Whereas, the latter is based onthe direct spreading at the fluid interface of a controlledvolume of a particle dispersion, leading to the formation ofa spread monolayer [9,10]. The interfacial density of parti-cles is controlled in the latter case by the spread amount,while for the adsorbed monolayers it depends strongly onthe particle affinity for the fluid interface.

This review is focused on providing a comprehensiveunderstanding on the fundamental bases underlying therelaxation mechanisms involved in the equilibration ofparticle-laden interfaces. For this purpose, we will startdescribing, firstly, the main physico-chemical aspects gov-erning the attachment of particles to fluid interfaces, and,subsequently their response when they undergo mechani-cal deformations. The last part of this review will providea briefly discussion on the application of particle-ladeninterfaces on the stabilization of dispersed systems.

It is worth mentioning that particles at fluid interfacesbehave in many aspects as surfactants [2, 48]. Thus, theuse of particles for replacing surfactants in technologicalapplications (foams and emulsions stabilization), has un-dergone a spectacular development in recent years. How-ever, the different length scales involved in particles andsurfactants, and the different nature of the attachmentof particles and surfactant at the fluid interface leads toimportant different in the physico-chemical behavior ofparticles and surfactants at interfaces.

2 Contact angle: controlling the particleattachment at interfaces

Despite the most fundamental bases governing the adsorp-tion of particles at fluid interfaces have been studied ex-tensively in the last thirty years, several aspects still re-main unclear and deserve further studies [1–3,6,12–14,44].This is mainly due to the multiphasic character of particle-laden interfaces which makes necessary to take into ac-count the role of three interfaces: two fluid/solid and onefluid/fluid (see fig. 1 for a schematic representation).

Fig. 1. Sketch representing the typical situation of a parti-cle attached to an arbitrary fluid interface in which θ repre-sents the contact angle or relative wettability of the particleby the interface, R is the particle radius, and γf1f2 , γpf1 andγpf2 are the interfacial tensions corresponding to the fluid/fluidinterface and the two fluid/solid (fluid/particle) interfaces,respectively.

The accumulation of particles at fluid interfaces re-sults from the complex balance between different types ofinteractions, with the electrostatic and capillary interac-tions playing a central role [1, 12, 34]. The result of suchbalance drives the particles until their equilibrium posi-tion in relation to the separation plane between the twophases defined by the interface, and allows one to definethe relative wettability of solid particles by the two fluidphases, i.e. the three phase contact angle θ or simply con-tact angle (see fig. 1).

The contact angle plays a role for the adsorptionof particles at fluid interface similar to that of theHLB (hydrophilic-lipophilic balance) in molecular species,defining the preferential partition of particles betweenboth phases [48, 49], which is related to an asymmet-ric distribution of the interactions through the two fluidphases [50, 51]. This leads to two limits cases, when thefluid phases present very different nature: θ = 0–10◦ andθ = 170–180◦. In those cases, the adsorption at the fluidphase is hindered and particles remain preferentially in thehydrophilic and in the hydrophobic phases, respectively.Therefore, it is possible to assume that partial wetting ofparticles for both fluid phases is a key factor on their ad-sorption at the fluid interface. Figure 2 shows a schematicrepresentation of the preferential distribution of particlesbetween the fluid phases as the contact angle changes.

The position of the particle in relation to the interfacialplane allows defining its hydrophilicity-hydrophobicity.When water/oil interfaces are considered, it is frequentlyto define particles as hydropilic for angles θ < 90◦, be-coming hydrophobic when θ > 90◦. It is worth mention-ing that the preferential distribution of particles betweenthe fluid phases plays an important role in the control ofthe relaxation mechanisms of particle-laden interfaces andconsequently in their technological applications [52,53].

The contact angle θ can be defined assuming the ex-istence of a mechanical equilibrium between the differentforces operating at the particle-laden interface. This con-

Eur. Phys. J. E (2018) 41: 97 Page 3 of 21

Fig. 2. Idealized representation of the relative position of anarbitrary particle in relation to the interfacial plane defined bythe fluid interface as function of its contact angle.

dition is given by Young’s equation [54,55]

0 = γpf2 − γpf1 − γf1f2 cos θ, (1)

which can be reordered as follows:

cos θ =γpf2 − γpf1

γf1f2

. (2)

Despite the role of the contact angle has been neglected instudies on particle-laden interfaces, from its definition it isevident its importance for controlling the balance of ener-gies at the interface. Thus, a reliable determination of thecontact angle of particles attached at fluid interfaces is akey for deepening on the complex phenomelogy occurringin this type of systems. This has stimulated the interestfor developing methodologies allowing for the determina-tion of this important parameter [4, 46, 47, 56–67]. It isworth mentioning that the above definition of the contactangle neglects the roles of the particle roughness and ofthe line tension, which affect significantly the adsorptionat fluid interfaces of nanosized particles [68, 69]. In par-ticular, the line tension modifies the energetic landscapeassociated with the attachment of particles at the inter-face. However, the role of the line tension decreases fastwith the increase of the particle size and, for most prac-tical cases, the attachment of particles at fluid interfacecan be described without considering the role of the linetension. For these reasons, no further discussion about itsrole will be included in this review. Further details on theeffect of the line tension in the attachment of particles tofluid interfaces can be found in refs. [67,70,71].

The attachment of particles to fluid interfaces is de-fined by the difference between the energies of a particle inthe bulk suspension and at the interface. For small spheri-cal particles, in which gravity effects can be neglected, theattachment energy, μw, is given by the following expres-sion:

μw = −πR2γf1f2 (1 ± cos θ)2 , (3)

where R is referred to the radius of the particle and the± sign indicates the position of the particles in relation tothe interfacial plane. Therefore, (+) is used for hydropho-bic particles that are centered above the interfacial plane,and (−) indicates the hydrophilicity of the particles which

Fig. 3. Dependence of the attachment energy on the contactangle for the adsorption of colloidal particles with differentsizes, R = 1 μm (a) and R = 10 nm (b), at an arbitraryfluid/fluid interface (γf1f2 = 50mN/m). Note the differencesin the values of the energy scale.

appears centered below the interfacial plane. Figure 3 rep-resents the attachment energies at an arbitrary fluid/fluidinterface corresponding to colloidal particles with two dif-ferent sizes.

Particles at fluid interfaces present an attachment en-ergy that overcomes in most cases several times the ther-mal energy kBT , with kB being the Boltzmann constantand T the absolute temperature [34]. The analysis ofeq. (3) evidences clearly that the reversibility or irre-versibility of the particle attachment depends on the size,R, chemical nature of the particles, θ, and on the nature ofthe interface, γf1f2 . In general, microparticles are trappedat fluid/fluid interfaces with energies 106–107 times kBTwhich almost ensure the irreversibility of their attachment.However, the situation is more complex when nanopar-ticles are considered, and the irreversibility of their ad-sorption is strongly dependent on particles size, appearingfor the smallest particles adsorption-desorption equilibriasimilar to those found for conventional surfactants [72].Wi et al. [73] pointed out that the attachment at fluidinterfaces of particles with diameter above 10 nm can beconsidered irreversible. It is worth mentioning that therevesibility or irreversibility of the adsorption of particlesat fluid interfaces represents a key role on the control of theparticle interactions within the interface and consequentlydetermines the equilibrium structure of the particle assem-bly [74]. The existence of an irreversible attachment doesnot mean that particles remain constrained at fixed posi-tion in a quasi-2D layer. They are free to diffuse along the2D plane defined by the interface. In addition, particles atfluid interfaces are undergone to continuous fluctuationsaround their equilibrium positions due to thermal and/orcapillary deformation of the interface.

The above discussion evidences the importance of par-ticles wettability on their adsorption at fluid interfaces.Particles wettability can be tuned through any methodol-ogy enabling for their surface modification [3], involving

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also changes on the chemical or physical nature of the par-ticles. The chemical modification is generally based on theirreversible attachment of ligands to the particles surfacethrough a chemical reaction that leads to the formation ofcovalent bonds, e.g. thiol onto gold surfaces or silanizationreactions of SiO2 [75–77]. The modification of particleswettability using physical procedures involves the inter-action between particles and chemical species, generallysurfactants (molecular or polymeric ones) [78, 79] but insome cases it can be used even low molecular weight alco-hols [80], through different types of interactions, e.g. elec-trostatic, van der Waals or hydrogen bond interactions.It is worth mentioning that in recent years the prepa-ration of particles with asymetric wettability, i.e. Janusparticles and patchy colloid, is attracting growing techno-logical interest in the preparation of particle-laden inter-faces [81–84].

3 Energetic landscape on the adsorption ofparticles at fluid interfaces

The control of the interfacial self-assembly of particles re-quires a detailed analysis of the energetic landspace be-cause the final microstructure and dynamics of particle-laden interface results, as was aforementiones, from an in-tricate balance involving different interactions [85,86]. Forparticles attached at fluid interfaces, it is possible to definethe energetic balance in terms of the difference betweenthe chemical potentials of the particles at the interface,μint, and in the bulk, μb [3]

Δμ = μint − μb, (4)

which can be splitted in different contributions

Δμ(φ, ϑ) = μw + μi(φ, ϑ) + μe(φ, ϑ), (5)

where μw, μi and μe are the components due to the par-ticle wettability, interactions and entropic contributions,respectively. φ and ϑ are the volume fraction of particlesin the bulk and the interfacial coverage, respectively. μw

is associated with the effect of the contact angle definedby eq. (3) and μe is the unfavorable entropic contributionassociated with the reduction of freedom degrees of theparticles resulting from their attachment to the interface.μi considers the different interactions occurring betweenparticles at fluid interfaces: van der Waals, electrostatic,capillary, fluctuations or hydrophobic. Such interactionsemerge from the inter-particle coupling and are stronglydependent on the inter-particle distance, i.e. particle den-sity. Attractive interactions favor the attachment of parti-cles at fluid interfaces, whereas the opposite is true whenrepulsive interactions are considered. It is worth notingthat the control of the assembly of particles at the in-terface is challenging because the inter-particle interac-tions occur through a discontinuous environment (inter-face), which defines an asymmetric distribution of the in-teraction through the different phases [51]. The balancebetween the aforementioned contributions determines theequilibrium coverage of the interface, ϑeq.

In this section we briefly describe the role of the mostimportant contributions affecting μi. These contributionscan be grouped in two different categories [51]. The firstgroup is related to the interactions appearing in bulk sys-tems, which are modified due to the presence of an inter-face. This is generally called direct interaction and involveselectrostatic, hydrophobic and van der Waals interactions.The second group includes the interactions appearing dueto the presence of an interface, with the capillary one be-ing its paradigm.

3.1 Direct interactions

The direct interactions occurring between colloids are cor-related to the specific nature of the particles. In the follow-ing, it is provided a briefly description of the most com-monly found in particles systems. There are other typesof interactions that can appear as consequence of specificproperties of the particles, e.g. magnetic or elastic. A de-tailed discussion on its effect can be found in the work byOettel and Dietrich [51].

3.1.1 Van der Waals interactions

For particle-laden interfaces, the analysis of the van derWaal interactions is more complex than for particles in thebulk, and can be performed defining an effective Hamakerconstant that depends on the volume fraction of particleimmersed in the fluid 2 (f = (1−cos θ)/2) [3,50,87]. Thus,considering an arbitrary interface the effective Hamakerconstant A reads as follows

A = Apf1 + f2(3 − 2f)(Apf2 − Apf1), (6)

where Apf1 and Apf2 define the Hamaker constants acrossfluid 1 and fluid 2, respectively. This allows one to assumethat the strength of van der Waals interactions of parti-cles attached at the fluid interfaces can depend on f , i.e.of the particle wettability. The average van der Waals in-teraction between a pair of particles at a fluid interfacecan be approximated as

EvdW = − A

12

(a

R − a

), (7)

where a defines the inter-particle distance. Recently, Diaset al. [88] have pointed out that a similar interaction po-tential to that provided by eq. (7) accounts for the changeson the growth mechanism of particle domains associatedwith the assimetric distribution of interactions appearingin interfaces formed by anisotropic particles [89,90].

3.1.2 Electrostatic interactions

Electrostatic interactions occur for charged colloids, andare the result of an intricate balance between the screenedcoulombic repulsion, typical of particles in bulk suspen-sions, and the long-range dipole-dipole interations due

Eur. Phys. J. E (2018) 41: 97 Page 5 of 21

to the particles attachment at the fluid interface. Thedipolar interactions depend on the nature of the fluidphases across which occur and, thus, they present a clearasymmetry associated with the presence of the interfa-cial plane [34]. For the part of the particles immersed inthe aqueous phase, the dipole is formed by the chargeson the particles surface and the counterions dissociated inthe bulk, whereas for the part of the particles inmersed inthe non-polar phase the dipole is formed between surfacecharges and image charges appearing in the water [50].The total interaction potential combining the electrostaticand the screened Coulomb interaction reads [91]

Eelectrostatic =a1kBT

3re−κr +

a2kBT

r3, (8)

where a1 and a2 are prefactors determining the role ofthe screened Coulomb potential and the dipolar interac-tion, respectively. For inter-particle distances long enough(κr � 10, where κ is the inverse Debye screening length),the role of the dipolar interaction is predominant [92,93].It is worth mentioning that electrostatic interactions arelinked to the appearance of electrocapillary interactionsassociated with the deformation of the interface due tothe action of electrostatic stresses [50].

3.1.3 Hydrophobic interactions

Hydrophobic interactions present special importance asthe size of the particles become smaller. This is explainedassuming that in such scale length the molecular detailsof the solvent and the interface start playing an importantrole. Thus, the hydrophobic interactions appear as resultof the necessity to minimize the unfavorable contacts be-tween the particles and the solvent [94–96]. Despite itsimportance, no systematic discussion on the role of thehydrophobic interactions in particle-laden interfaces canbe found in the literature yet.

3.2 Interactions due to the presence of the interface

The main interactions due to the presence of the interfaceare the capillary ones. These interactions emerge from thedeformation in the direction perpendicular to the fluid in-terface associated with the adsorption of particles. Thisoriginates strong lateral interactions (attractive or repul-sive) between colloids. For big particles, gravity is able toinduce the deformation of the interface, leading to the so-called flotation forces which decrease strongly with size.These forces are irrelevant when particles are smaller thanthe interface capillary length because the weight of theparticles is too small to induce any significant deforma-tions of the interface. However, for small particles the ap-pearance of other type of capillary forces, the so-called im-mersion forces, is found. These forces are the consequenceof the perturbation of the interface, and present an at-tractive character over a broad range of length scales. The

capillary interactions can be written as a function of thedeformation amplitude of the interface H as follows [97]:

Ecapillary(R) = −12πγf1f2H2ζ

r4

R4, (9)

where ζ is a factor depending on the particle orientation.For charged colloids, electrocapillary forces can appeardue to differences in the dielectric constant between thetwo phases, leading also to an the interface deformationcomparable to that resulting from the gravity [51,98].

The above discussion presents so far the most impor-tant aspects related to the interactions of particles at fluidinterfaces. There are other types of interactions that canemerge from the specific properties of the colloids, e.g.elastic, steric or magnetic. However, a comprehensive ex-planation of the role and origin of the different types ofinteractions involved in the energetic balance of particle-laden interface is far from the scope of this review, furtherdetails on this topic can be found in previous works byGarbin et al. [3], Bresme and Oettel [51] and Deshmukhet al. [99].

4 Thermodynamics and structural aspects ofparticle-laden fluid interfaces

It was discussed above that probably the most importantfeature determining the attachment of particles at fluidinterfaces is their surface nature, i.e. their HLB. However,particles adsorption presents a main difference with theadsorption of surfactant at fluid interface, which comesfrom the almost irreversible character of the attachment ofparticles to the fluid interface [72]. Furthermore, the signif-icant difference existing between the sizes of particles andsolvent molecules is an additional difficulty for providingan accurate theoretical description of the thermodynamicsbehavior of particle-laden interfaces. The aforementionedaspects limit the application of the classical equations ofstate, e.g. Langmuir, Frumkim, etc., in particle monolay-ers [100]. Hence, the development of new thermodynam-ics models accounting for the physico-chemical behaviorof particle-laden interfaces is required [101,102].

According to our knowledge, the first thermodynamicsmodel accounting for the behavior of particle-laden inter-faces was proposed by Binks [48]. This model was based onthe Volmer and van der Waals equations, assuming thateach single particle behaves as a surfactant molecule. Thisleads to consider that the area occupied by a single parti-cle at the interface is equivalent to its geometric area, andconsequently it may be expected that the surface pressureΠ = γ0 − γ (with γ0 and γ being the surface tension ofthe bare fluid interface and of the particle-laden interface)remains close to zero until the system present hard-spherebehavior (close-packed monolayer). Such contradiction be-tween experiments and theoretical predictions evidencesthat the role of the interactions occurring at the interfacecannot be neglected. Thus, the strong differences exist-ing between particles and common surfactants, especially

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Fig. 4. Comparison between experimental results (symbols)and theoretical predictions (lines) for particle-laden interfacesformed by bare particles (Δ) and steric-stabilized particles (�).Reprinted with permission from ref. [102]. Copyright (2006)American Chemical Society.

related to the different length scales involved in their in-teractions, leads to unrealistic predictions of the depen-dence of the surface tension on the interfacial coverage,e.g. according with the commented model it is expectedthat only small particles (diameter < 1 nm) at relativehigh interfacial coverage (50–70% of the total interfacialarea) can lead to a significant change of the surface pres-sure. Some of the limitations of the aforementioned modelwere overcome by Miller et al. [101]. Their description ofthe interfacial behavior of particle-laden interfaces followstheoretical assumptions similar to previous models usedfor the description of protein layers [103], including pa-rameters regarding the particle nature. This model pro-vides an expression for the surface pressure isotherm ofparticle-laden interfaces that reads as follows:

Π =kBT

ω0

[ln

(1 − ω

A

)+

(ω

A

)]− Πcoh, (10)

where ωA is a term accounting for the coverage of the in-

terface and ω0 represents the area of a particle. Πcoh isthe so-called cohesion pressure, which measures the inter-actions occurring within the particle-laden interface. Eventhough the above discussed model has been used for a re-duced number of systems, the available results foretellsa good agreement between experimental results and the-oretical predictions, at least for particle monolayers wellbelow of collapse, independently on the nature or size ofthe particles (see fig. 4).

A more recent model enabling for the description of thethermodynamic behavior of particle-laden interface wasproposed by Groot and Stoyanov [104]. They developeda model which included features of the interaction po-tential on the dependences of the surface pressure on theinterfacial coverage, leading to an expression that reads as

follows:

Π =4kBT

πd2

[byZ

λ− b2y

2

], (11)

where d represents the distance within the occuring long-range interactions, Z is the compressibility factor [105,106],

√λ represents the effective diameter of the parti-

cles, y represents the interfacial coverage and b and b2

are interaction parameters associated with the used po-tential. This theoretical model has been applied satisfac-torily by Deshmukh et al. [107] for describing the behav-ior of soft particles attached at fluid interfaces. It is worthmentioning that the aforementioned models are applicablein most cases to spread monolayers in which the relation-ship between surface pressure and interfacial coverage isknown [78,79,105,108–112].

A complete description of the interfacial behaviorof particle-laden interfaces requires some considerationsabout morphological and structural aspects. For the studyof these aspects, it is possible to assume two different ap-proachs: the first one relies on the determination of theparticle distribution within the quasi-2D interfaces, i.e.the study of the interfacial morphology. The second ap-proach requires the analysis of the position of the particlesin relation to the interfacial plane, i.e. the determinationof the contact angle.

Santini et al. [46] study the interfacial morphol-ogy of silica nanoparticles decorated with CTAB (hex-adecyltrimethylammonium bromide) using Brewster An-gle Microscopy (BAM), and conclude that particles hy-drophobicity plays a key role on the control of the layercoverage, as was evidenced from the differences in the in-terfacial textures. Following with the same system Mae-stro et al. [47] showed that the wettability of the particles,and consequently the position of the particles in relationto the interfacial plane, could be also modified by the de-gree of hydrophobicity of the particles. Similar results werefound by Zang et al. [56] using silica hydrophobized bychemical silanization. These above results confirm that theimportance of the particles wettability in their position inrelation to the interfacial plane.

The study of the adsorption of monolayers of silicananoparticles decorated with palmitic acid at the wa-ter/vapor interface showed results in agreement with thosediscussed above [113]. For particles with the lowest hy-drophobicity, isolated aggregates of particles were foundat the interface which coalesce as their hydrophobicity isincreased, leading to the formation of close-packed particlemonolayer. Such behavior is associated with the increaseof the interfacial coverage which leads to a sharp decreaseof the surface tension with a strong decrease of the sur-face tension. Figure 5 shows the interfacial textures, sur-face tension isotherm and thicknesses of monolayers of sil-ica nanoparticles decorated with palmitic acid at the wa-ter/vapor interface obtained increasing the concentrationsof palmitic acid, i.e. particles with increasing hydropho-bicity. Santini et al. [110], using ellipsometry, showed thatthe densification of the layer evidenced by BAM was as-sociated with an increase of the layer thickness, i.e. of thesurface concentration of particles at the interface. This lat-

Eur. Phys. J. E (2018) 41: 97 Page 7 of 21

Fig. 5. Interfacial textures obtained by BAM, layer thick-ness, h, and surface tension for the adsorption of dispersionsof silica nanoparticles decorated with different concentrationsof palmitic acid at the water/vapor interface. Adapted fromref. [56]. Reproduced by permission of the PCCP Owner Soci-eties.

ter is in qualitative agreement with the results found bythe group of Noskov [114–118] for polystyrene sulfate la-tex micro- and nanoparticles and silica nanoparticles dec-orated with CTAB at both water/vapor and water/alkaneinterfaces. The above results allow concluding that the in-crease of the particles hydrophobicity drives the transitionfrom layer with a lost packing to close-packed particle-laden interfaces.

The main problem when nanoparticles are consid-ered is the impossibility to analyze the packing of eachsingle particle at the interface. However, this is solvedwhen microparticles are studied because their sizes allowcharacterizing their positions using microscopy analysis.Bonales et al. [10] carried out an interesting phase dia-gram of microparticles of polystyrene sulfate latex at thewater/octane interface. Their results agree qualitativelywith the above discussion on the densification of the in-terfacial layers of nanoparticles. However, they were ableto observe the appearance of transitions between severalphases as the interfacial coverage increases. Such transi-tions appear independently of the particle size, and only aslight shift of the critical coverage needed for the tran-sition is observed with the change of the particle size.Similar studies were carried out by Parolini et al. [119],leading to conclusions in good agreement with those pre-viously obtained by Bonales et al. [10]. Studies on binarymonolayers of colloidal particles were also carried out byBonales et al. [9], and their results pointed out that thephase behavior of the mixed systems appear as intermedi-ate between that of the individual systems. An interestingway to modify the structure of particle-laden interface isby the mean of physico-chemical stimuli. This was shownby Martınez-Pedrero et al. [120] using the magnetic re-sponse of superparamagnetic microparticles.

5 Anisotropic particles at fluid interfaces

The above discussion has mostly concerned to the behav-ior of spherical and nearly spherical particles trapped atfluid interfaces. However, in recent years a growing inter-est on the study of the interfacial behavior of anisotropicparticles has been developed [121, 122]. Asymmetry de-fines the orientation-dependent interactions at the in-terface which modify the particle assembly and, conse-quently, the properties of particle-laden interfaces. Fur-thermore, the stability of particles trapped at fluid in-terfaces is correlated to the geometry, existing a criti-cal aspect ratio beyond which particles are not stableat fluid interfaces. In general, elongated particles presentless stability at the interfaces than particles having anyother geometries. This behavior is ascribable to the highervalues of line tension [50]. Loudet et al. [123] evidencesthat the wetting properties, i.e. mainly the line tension,is strongly correlated to the aspect ratio of nanoparti-cles. This has driven an important research for optimiz-ing the organization of rod-like particles and carbon nan-otubes at fluid interfaces which requires controlling thesurface chemistry of the particles to reduce the line ten-sion below a threshold value about 0.1 nN [50]. Kimet al. [124] studied the phase behaviour at interfaces ofBaCrO4 nanorods and evidenced the existence of richphase behaviour (isotropic, 2D nematic, 2D smectic and3D nematic) as the interfacial density increases. Similarstudies were carried out by Hernandez-Lopez et al. [125]using carbon nanotubes.

Considering the interactions involved in monolayers ofanisotropic particles, it is expected that at short distancethe shape can influence the steric and van der Waals in-teractions. However, the behaviour becomes more complexat long distance mainly due to the effect of the particlegeometry in the deformation of the interface, i.e. in thecapillary forces [50]. Loudet et al. [126] studied the assem-bly of micron-sized ellipsoidal particles at fluid interfacesand found that the asymmetry of interactions occurring atthe interface determines the formation of open branchedaggregates of particles with a high tendency to the for-mation of particles chains due to the directionality ofthe interactions existing at interface [121]. This behaviourcontrasts with that found for spherical colloids at fluidinterfaces in which the formation of close-packed struc-tures is found [10]. The shape dependence of the interfa-cial organization of colloids at the interface is explainedassuming the different nature of the capillary interactionsinvolved. For non-spherical particles, a long-range capil-lary interaction of quadrupolar origin, largely exceedingthe thermal energy (kBT ), accounts for the complex in-terfacial assembly [126, 127]. It is worth mentioning thatcapillary interactions in anisotropic particles at fluid in-terfaces overcome several times than in the case sphericalparticles [121, 122, 126]. The above landscape evidencesthat interactions between non-spherical particles is muchricher than that found for spherical colloids, leading to amore complex interfacial organization [50].

Deepening on the assembly of anisotropic particles atfluid interfaces, Botto et al. [128] showed that the specific

Page 8 of 21 Eur. Phys. J. E (2018) 41: 97

geometry of the particles affects dramatically the ener-getic landscape and, consequently, the interfacial assem-bly. This drives the assembly of ellipsoidal particles fol-lowing a side-to-side configuration to form flexible chains,whereas the assembly of cylinders occurs in an end-to-endconfiguration that leads to the formation of rigid chains.This is explained considering that capillary interactionsare strongly influenced by the geometry of the particles,which can be exploited to obtain interfaces with a broadrange of properties.

An additional aspect to take into account when theassembly of anisotropic particles at fluid interfaces is con-sidered is the preferential orientation. The existence of apreferred direction for the adsorption of colloidal particlesat fluid interfaces was demonstrated by Isa et al. [129] us-ing contact angle measurements of polymeric dumbbellsin which each lobe presents a different wettability for thephases. The results evidence that the preferred orientationfor the adsorption of dumbbells was in tilted configuration.In a similar way, the adsorption and assembly of patchycolloids present a preferential orientation which is associ-ated with the opening angle of the patches [130–132].

It is worth mentioning that the progresses on the un-derstanding of the interfacial organization and propertiesof assemblies of anisotropic particles is more difficult thanfor spherical particles, mainly because of the complicatedfabrication process of anisotropic shapes particles undercontrolled conditions.

6 Dynamics of particles at fluid interfaces

The understanding of the dynamics of particle at fluid in-terfaces requires considering both the inter-particle andthe particle-solvent interactions. Therefore, the motion ofcolloids attached to fluid interfaces is strongly dependenton the hydrodynamics constrains associated with the pres-ence of the surrounding fluid, which determine, in most ofthe cases, the time-scales governing the behavior of parti-cle attached at fluid interfaces [133–139].

At the shortest time, the fluid phase presents acompressible-like behavior and the colloidal motion leadsto a density fluctuation similar to a sound wave, with itscharacteristic time being defined by ts = R/cs, where Rand cs represent the radius of the colloid and the velocityof sound, respectively. The time-scales involved in this mo-tion are extremely short around 10−1 ns, and thus it can-not be measurable with most of conventional techniques.

A second time, th, is associated with hydrodynamicsinteractions. The colloidal motion origins a tranverse mo-mentum diffusing away from the particles. The originatedvelocity field induces a drag force between the particles.The time-scale involved in this process is around 10 nsthat is equivalent to the time required for the tranversemomentum to diffuse along the typical inter-particle dis-tance which is comparable to the diameters of the col-loids. Coupled with the motion due to the hydrodynamicsinteractions appear other dynamics associated with thedecay of the initial velocity of a colloid. These are a con-sequence of the effects provoked on the particles by the

action of time-dependent velocity fields appearing in fluidsdue to particle motion. The time-scales of these dynamicsare governed by the diffusion coefficient of the transversemomentum of the fluid.

When colloids are considered, they present a diffusion-controlled motion with a typical diffusion constant definedby D0 = kBT/g, where g is the Stokes friction coefficient.The characteristic time for the motion of colloids at theinterface along a distance similar to their radius appearsin the range 10−3–1 s. This evidences clearly the separa-tion between the diffusion of colloids and other motions.Thus, it is possible to assume that the motion of colloidscan be considered as an uncorrelated Brownian motion inthe long-time limit. However, it is worth mentioning thatthis approach presents some limitations because the dif-fusion of each single colloid depends significantly on theconfiguration of its neighbor due to the occurring interac-tions.

The analysis of the particles trajectories at fluid inter-faces by videomicroscopy provides information related tothe dynamics involved in the particle-laden interface. Thisinformation can be obtained from the calculation of themean square displacement, MSD (〈Δr2(t)〉), which is re-lated to the diffusion coefficient, D, and the characteristiclength of the translational motion, as follows:

⟨Δr2(t)

⟩= 2dDtα, (12)

where α is a scale exponent. Considering particle monolay-ers with low coverage, it can be expected a linear depen-dence of the MSD on t, and the characteristic diffusiontime can be easily obtained according to eq. (12) fromthe slope of the representation [6, 140, 141]. However, thedensification of the monolayers drives the transition to amore complex dynamics regime, and a clear differentia-tion between the short-time and long-time dynamics ap-pears. This difference is characterized by a change of theslope which can be explained assuming that in the short-time limit, particles diffusion is constrained to the regionlimited by their closer neighbor, leading to a short-timeself-diffusion coefficient defined as follows:

Ds = limt→0

〈Δr2〉4t

. (13)

The diffusion coefficient in the short-time limit decreasesas the surface coverage, ϑ, of the particle-laden interfaceincreases as result of the interactions Ds = αD0(1 −μϑ), where μ is a parameter depending on the interac-tions [142]. In the long-time limit, the collective motionof particles start to play a role on the dynamics of theparticle-laden interface and it is possible to define a diffu-sion coefficient in the long-time limit as follows:

Dm = limt→∞

〈Δr2〉4t

, (14)

The process defined by the long-time dynamics responseon particle-laden interfaces can be rationalized by par-ticles escaping from their cage, delimited by their near-est neighbors, the so-called α-relaxation [143–145]. When

Eur. Phys. J. E (2018) 41: 97 Page 9 of 21

the interfacial density is high, the inter-particle repulsionsleads to arrested dynamic within the experimental acces-sible time windows. Under these conditions there are noanalytical results and the results are analyzed in terms ofthe harmonically bound independent Brownian oscillator(BHO), in which particles behavior obeys to the Langevinequation including an elastic force [146,147]

mdv

dx= −gv + F (t) − kx, (15)

with m being the mass of a particle, v represents its ve-locity and k the characteristic force constant of the elasticforce acting on the particle. F (t) represents the randomforce. Considering the overdamped limit, and neglectingthe role of the inertia, the model leads to the followingsolution [143,144]:

⟨Δr2(t)

⟩= 2dδ2

[1 − e−D0t/δ2

], (16)

where δ2 = kBT/k. The characteristic time is defined astBHO = δ2/D0 = g/k. Several ad hoc corrections havebeen introduced to the above equation in order to de-scribe the dynamics of interacting Brownian particles. Amore complete description is given by the following equa-tion that accounts for a non-expontial character of thedecay [148,149]:

⟨Δr2(t)

⟩= 2dδ2

[1 − e−(D0t/δ2)c] (

1 +D0t

δ2

). (17)

Equation (17) introduces a stretching exponent c, and aterm accounting for long-term dynamics of particles es-caping from particles groups, which recovers the lineardependence on time. The stretching exponent is a fittingparameter, assuming values lower than 1 and accounts forthe width of the spectrum of relaxation time.

For monolayers showing a solid-like character, theabove model is no longer applicable, and it is needed to de-velop a new model. The Overdamped Bead-Spring model(OBS) accounting for particle dynamics under high den-sity conditions reads as follows [150,151]:

mdvi

dt= −gvi(t) + Fi(t) − k

nn∑j

[uj(t) − ui(t)] , (18)

where ui(t) is the displacement of the particle i at time t,and nn is the number of nearest neighbors of particle i.The high density of particles existing in solid-like mono-layer hinders the escaping dynamics of particles from thegroups, and thus the MSD does not present any linearincrease at long times. The solution of the above modelreads

⟨Δr2(t)

⟩=

2dkBT

kN

∑b

1L(qb)

[1 − e−kL(qb)t/b

]. (19)

The above equation only considers the interaction betweencloser neighbors. L(qb) =

∑nnj [1−cos(qxnj)] is the lattice

factor, with qb being the b-th wave vector of the relaxationmode q, and nj takes into account a vector pointing fromthe point i of the lattice to its closer neighbor j. The OBSmodel leads to a similar slope in the MSD than the BHOone in the initial stages, and tends to a limit value definedby

limt→∞

⟨Δr2(t)

⟩(t → ∞) =

2dkBT

kN

∑b

1L(qb)

, (20)

The long limit depends on both the strength of the har-monic force and the lattice factor.

7 Rheological response of particle-laden fluidinterfaces

This section is devoted to explain the response of particle-laden interfaces against mechanical perturbations, payingspecial interest on the relaxation mechanisms of micro andnanoparticles [6, 40, 41, 152–155]. A deep understandingon the mechanical properties of particle-laden interfaces,hence, might be a key to understand and improve manytechnological applications associated with the interactionof particles and interfaces, e.g. phase transfer catalysis,encapsulation, enhanced oil recovery or emulsification andfoaming [156].

7.1 Dilational rheology

Dilational rheology experiments provide information onthe changes induces on the surface tension due to themodification on the interfacial area. Thus, it is possibleto assume that infinitesimal changes of the area of theinterface, δA(t), due to an uniaxial stress leads to a time-dependent change of the surface pressure defined by δΠ(t),which could be defined as follows [157]:

δΠ(t) = Π(t) − Π0 =∂Π

∂AδA = −ε(t)u(t) (21)

with ε(t) = −A0(∂Π/∂A)T representing the time-dependent dilational modulus. The above equation is ageneral time-dependent response function, where the sur-face stress δΠ results from a perturbation given by a com-pression strain u(t) = δA/A0. For fluid films at equilib-rium, the dynamic modulus is equal to the Gibbs elasticityε0:

ε(t) → ε0 = Γ

(∂Π

∂Γ

)eq

, (22)

where Γ = 1/A is the surface concentration. For small-amplitude oscillatory deformation with frequency ω, thecomplex modulus reads as

ε(ω) = ε′(ω) + iωκ(ω). (23)

where the real part ε′(ω) corresponds to the storage mod-ulus and the imaginary part ε′′(ω) = ωκ(ω) is referred to

Page 10 of 21 Eur. Phys. J. E (2018) 41: 97

the loss modulus, being κ the interfacial dilational viscos-ity. The definition of the viscoelastic dilational modulusallows expecting modifications either on the adsorptionstate of the particles at the fluid interface or on the struc-ture of the interface as a consequence of the stress inducedby the deformation. Different relaxation dynamics charac-terized by different time-scales can appear as response toa dilational perturbation of the interfacial area [109,158].

Despite the big number of experimental and theoreticalstudies dealing with the response of particle-laden inter-faces against dilational stresses, there are many aspectsthat remain unclear, especially when theoretical predic-tions and experimental results are compared [6, 11, 101,109].

On the best of our knowledge, the first study dealingwith the response to dilational stresses of particle-ladeninterface was carried out by Miller et al. [101]. They stud-ied the relaxation of particle-laden films on the basis oftheoretical models similar to those generally used for de-scribing the interfacial behavior of proteins and proteins-surfactant systems [159, 160]. This framework provides adescription of the mechanical response of particle-ladeninterfaces on the bases of the information obtained fromtheir adsorption isotherms. However, this study remainsas a mainly theoretical one and no further advancementson the application of the aforementioned model to exper-imental results have been performed yet.

As was already mentioned, the attachment of particleto fluid interfaces is strongly correlated to their wettabil-ity, thus it is expected that this parameter may presentan important effect on the dilational response of particle-laden interfaces. Safouane et al. [161] explored the dila-tional response of fumed silica nanoparticle monolayersat the water/vapor interface using capillary waves in thefrequency range 200–990 kHz and found that the rheologi-cal response was influenced by the interfacial morphology.However, they carried out that independently of the hy-drophobization degree of the nanoparticles and the surfacecoverage, the elastic component of the response was higherthat the viscous one and increases with the hydrophobicityof the particles due to their favored incorporation to theinterface. This rigidification of the film associated with itsdensification is explained considering an enhancement ofthe inter-particle interactions as was pointed out by Zahnet al. [162]. When the loss modulus is analysed, no depen-dences on the wettability or interfacial concentration ofthe layer were found.

Zang et al. [45] extended the studies by Safouane etal. [161] to the low frequency range and found the exis-tence of a relaxation process on a time-scale comparableto 1000 s. This process was associated with the reorganiza-tion of particles at the interface and becomes faster as thehydrophobicity of the nanoparticles decreases. This couldbe explained assuming the smaller surface coverage of theinterface as the particles hydrophobicity decreases, thusit is expected a favoured reorganization of the particlesat the fluid interface due to the reduced steric hindrance.Furthermore, they found that spread layers present lowerrigidity than compression one. This is explained consider-

ing that the latter present non-equilibrium arrested statesthat lead to the emergence of additional relaxation pro-cesses to the particle-laden interface [45,163].

Beyond silica nanoparticles, the rheology of latexmicro-particles spread at fluid interfaces have been widelystudied in recent years [114,115,155,164]. Kobayashi andKawaguchi [164] studied latex particles spread at the wa-ter/vapor interface and found that the particle-laden in-terface presents a viscoelastic behavior independently ofthe strain rate. In addition, they found a certain hystere-sis that is associated with the lost connection betweenparticles in the monolayers. The increase of the storageand loss moduli was found with the densification of themonolayer. However, once the coverage reaches a criticalvalue (at Π ∼ 15mN/m), both start to decrease steeply.This is explained considering the possible buckling of themonolayer that distorts the 2D packing of the monolayer.From the frequency dependences of the storage and lossmoduli the transition from a mainly fluid-like behaviorto a solid-like one was found, which is correlated to thestructural scenario found by Bonales et al. [10]. Deepen-ing on the correlations between the dilational responseand structural richness of the particle-laden interfaces, delRio et al. [165] found that the dilational modulus presentsan important correlation to the region of the phase di-agram studied, with the storage modulus being alwayshigher that the loss modulus. For low surface pressure,the storage modulus increases with the monolayer den-sification whereas the loss modulus remains constant atvalues close to that of the water. This could be explainedon the basis of the important role of the repulsive electro-static interactions between particles. The storage modu-lus presents a sharp increase till values around 350mN/m.This results in the formation of close-packed a monolayeras was evidenced by BAM imaging. When the electro-static repulsion is so high, the storage modulus can reachvalues until 600mN/m. This is explained assuming thepresence of a small number of defects in the close-packedmonolayer. In agreement with the result by Kobayashi andKawaguchi [164], del Rio et al. also found a decrease of thestorage and loss moduli for the highest surface pressuresdue to the breaking of the 2D packing of the interface.Qualitative similar results to those found for water/vaporinterfaces were found when latex monolayers at water/oilinterface were considered [114, 115]. It is worth mention-ing that particle-laden interface present a relatively smallrange of linearity on their dilation response, which makesnecessary to apply low strains deformations on the studiesof particle-laden interfaces [155].

The dilational rheology of monolayers formed by themixture of particles and surfactant has been studiedin more detail than that of monolayer formed only bynanoparticles. This can be in part ascribed to the ver-satility of the use of surfactants for modifying particleswettability [11]. It is expected that the interaction oftwo components bearing oppositely charged in solutioncan presented important effects on the interfacial prop-erties of such mixture, e.g. the appearance of synergeticeffects on the surface tension decrease due to the ad-sorption of the complexes formed in the bulk [166–169].

Eur. Phys. J. E (2018) 41: 97 Page 11 of 21

Fig. 6. Wide range dilational response of silica nanoparticles(1 wt%) decorated with CTAB (0.05 mM) at the water/vaporinterface as were obtained combining different experimentaltechniques. (a) Dependence of the elastic modulus on the de-formation frequency. (b) Dependence of the viscous moduluson the deformation frequency. Reproduced from ref. [109] withpermission from The Royal Society of Chemistry. Copyright(2011).

However, this is not always true as was evidenced byRavera et al. [78] studying mixtures of silica nanopar-ticles and CTAB. Other noticeable effects of the inter-actions were found in the dilational response in the lowfrequency limit (0.005–0.2Hz): 1) higher elasticity of theparticle-laden interface than the monolayer of pure surfac-tant and 2) strong dependence of the viscoelastic responseon frequency. Furthermore, it was found a stronger ef-fect of the particles adsorption at the water/oil interfacethan in the water/vapor interface. A more detailed study,concretely in a broad frequency range (10−3–103 Hz), ofthe rheological response of the aforementioned system ev-idenced two different relaxation processes of the interfa-cial layer related to the diffusion of the particles from thebulk to the interface and the reorganization of adsorbedmaterial at the interface [108,109] (see fig. 6). The resultswere described in terms of a mixed rheological mechanismconsidering a diffusion process and arbitrary kinetics oc-curring at the interface.

There are other works dealing with the study of therheological response of mixtures formed by CTAB andsilica nanoparticles which have evidenced the role of thecomplex balance of interactions in the control of the rheo-logical response. The most important interactions can beascribed to the CTAB depletion, the electrostatic and hy-drophobic interaction controlling the wettability of parti-

cles and the interactions between particles in the bulk andat the interface [46,47,170].

It is also important to consider the rose of the inter-facial aging on the mechanical response of particle-ladeninterfaces. This leads frequently to an increase of the di-lational elasticity for layers at both water/vapor and wa-ter/hexane interfaces [108, 116, 117]. Despite this rigidifi-cation process induced by the aging, no changes on sur-face tension was evidenced which is ascribable to the irre-versible attachment of the particles at the interface. Therigidification results from the formation of solid-like lay-ers as was evidenced by BAM images [116]. The elasticmodulus found for solid-like monolayers is comparable tothose found in latex monolayers [164,165]. This result wellagrees with the results found in order systems by Whitbyet al. [171] and by Santini et al. [108].

Other particle-laden interfaces that deserve specialattention are those formed by lipid and nanoparticles.These systems present big interest due to their useful-ness as model for studying the potential toxicity of in-haled particles. However, a detailed discussion of the rhe-ology of such systems is far from the scope of this re-view [25,26,172–180].

7.2 Shear rheology

Shear deformations are completely decoupled from anyother interfacial mode, i.e. their amplitude and time evo-lution are independent [181, 182]. For a typical in-planedeformation it is possible to provide a definition of theshear elasticity as the constant of proportionality betweenthe applied strain (uxy) and the stress (σxy). It is ex-pected that the description of “solid” films can be carriedout in terms of a Hookean behaviour characterized by theaforementioned proportionality: σxy = G uxy. For totally“fluid” films, the behaviour is described by it viscous char-acter: σxy = η duxy/dt, where duxy/dt defines the strainrate and η the interfacial viscosity. The viscoelastic pa-rameters (G, η) are increased by the presence of attrac-tive interaction between the species at the interface. Thiscan be explained considering that part of the energy isneeded to overcome the interaction, allowing the flow ofthe surface elements. Considering an oscillatory deforma-tion, it is possible to define the complex shear modulusG∗ as follows:

G∗(ω) = G′(ω) + iG′′(ω) ≡ G′ + iωη (24)

with G′ and G′′ representing the storage and loss moduli,respectively. For small-amplitude oscillatory deformationswith a fixed frequency ω it is possible to correlate theloss modulus and the viscous friction G′′ = ωη, whereη is the interfacial shear viscosity. The understanding ofthe response against shear perturbation of particle-ladeninterfaces has been strongly developed in the last years dueto their recognized impact in many aspects involving thesesystems [6,12]. This has fostered the research on this fieldto provide a detailed explanation about the correlationexisting between the response against shear of particle-laden interfaces and the morphology of the layers. It is

Page 12 of 21 Eur. Phys. J. E (2018) 41: 97

worth mentioning that the interactions between particlesare the main parameters affecting the shear response ofthe monolayers [183].

One of the first studies dealing with the characteriza-tion of the shear response of particle-laden interfaces wascarried out by Cicuta et al. [184]. They studied mono-layers of polystyrene latex (3μm of diameter) at the wa-ter/decane interface and found that, in contrast with thatfound when the dilational response was analysed, the lay-ers present a mainly viscous character with G′′ > G′. Thisis different to that found for β-lactoglobulin layers whichpresent a mainly elastic behaviour due to the possibilityto be deformed and compressed as response to the com-pression. Furthermore, it was found a sharp increase ofthe viscoelasticity of particle-laden interface for surfacecoverages overcoming the 75–80% of the total area, whichis associated with a jamming of the 2D film. It is worthmentioning that the differences in the existing interactionsbetween particle-laden interfaces and particles in the bulkdefine the different shear behaviour between particle-ladeninterfaces and their bulk counterparts [185].

Reynaert et al. [186] explored the correlations existingbetween interfacial structure and rheological response inparticle-laden interfaces and found that an interfacial ag-gregation leads to a shear response similar to that found inthe bulk systems, which confirms the important effect ofthe interactions in the control of the rheological response.This was later confirmed by Wijmans and Dickinson [187]by Brownian dynamic simulations.

Imperiali et al. [188] studied the effect of the interfacialcoverage on the shear response of asymmetric particles asgraphene oxide, and found that the different freedom ofthe particles to reorganize at the fluid interface plays acentral role on their shear response. Thus, at low fractionof coverage, the interface presents a reminiscent behaviourof 2D-platicized systems, whereas close-packed monolay-ers evidenced a perfectly elastic behaviour. Similar de-pendences of the shear response on the interfacial cover-age were found by Barman and Cristopher [189]. Theyfound a transition from shear thinning behaviour to yield-ing one with the increase of the interfacial density. This isexplained on the bases of the differences in the mechanisminvolves in the dissipation of the viscous stresses. Further-more, the response becomes non-linear with the increase ofthe surface coverage; with the viscoelastic modulus follow-ing a power law dependence on the surface coverage [186].

Deepening the role of the particle morphology on theinterfacial shear response, Madivala et al. [190] stud-ied ellipsoidal polystyrene particles at both water/decaneand water/vapor interfaces. They found that the differentstrength of the electrostatic interactions determined differ-ent interfacial structures. In the case of water/decane in-terfaces, particles arrange forming structures in which in-dividual particles coexist with linear aggregates, whereasat the water/vapor interface particles are organized form-ing flower-like aggregates. The differences in particles or-ganization leads to strong differences in the responseagainst shear of the particle-laden interface, which is anadditional evidence of the correlations existing betweenthe self-assembly of particles at the fluid interface and the

mechanical response of particle-laden interfaces. In con-trast to that found for spherical particle, the response ofasymmetric particle monolayers at the water/decane in-terface to shear deformation is mainly elastic, with a vis-coelastic modulus increasing with the packing modulus.When particles at the water/vapour interface are consid-ered, lower values of the shear elasticity were found. It isworth mentioning that the elasticity of ellipsoidal particlesat fluid interfaces is relatively high, even when the surfacecoverage is small, which differs from the above discussedbehaviour when spherical particles are considered [184].These differences between ellipsoidal and spherical parti-cles are associated with differences on the interfacial re-laxation mechanisms [191]. Ellipsoidal particles present abuckling transition, which does not appear for sphericalparticles, when the interfacial coverage is high. Such differ-ences on the rheological response are associated with therichness of the interfacial phase behaviour of non-sphericalparticles. The complex balance of interactions given theparticular aggregation pattern at fluid interfaces governsthe rheological response of particle-laden interfaces, e.g.the shear modulus of colloidal crystals formed by param-agnetic particles was found to increase with the strengthof the inter-particle repulsion [162].

The role of particles morphology on the shear responsewas also studied by Brown et al. [192] using non-sphericalparticles with different aspect ratio. In all the cases, shearthickening phenomena were found. However, the increaseof the asymmetry of the particles leads to a decrease of thethreshold coverage in which interfacial particles jammingoccurs. Furthermore, asymmetric particles can present abehaviour that may be reminiscent of the formation ofnon-equilibrium trapped layers, affecting the shear flowsat the interface. This is correlated to the particle chargeand the interfacial coverage [193,194].

Another important parameter affecting the rheologi-cal response of particle-laden interface is the roughness ofthe particle surface [195]. The roughness presents differenteffects on the rheological response of the particle-laden in-terface depending on the interfacial coverage. For low den-sity monolayers, the surface roughness reduces the shearviscosity, whereas the opposite is true when monolayers inthe vicinity of the jamming transition are considered. Thisis explained as result of the inter-particle friction as wasdemonstrated by Brown et al. [192], which plays an im-portant role for emulsion behaviour [196]. The importanceof the heterogeneity of particle surface for its trapping tofluid interfaces have been recently demonstrated by Zaniniet al. [197]. They showed that surface roughness can leadto the attachment of particles in metastable positions dueto the pining of the contact line, with such metastablepositions being able to be far from the real equilibriumposition. Thereore, the surface roughness may induce thathydrophilic particles behaves as hydrophobic ones and theopposite situation, providing the bases for stabilizing wa-ter in oil or oil in water emulsions in the same water-oilmixture using only a single type of particles.

As can be expected from the above discussion, par-ticle wettability plays also a relevant role on the rheo-logical response of particle-laden interfaces due to its im-

Eur. Phys. J. E (2018) 41: 97 Page 13 of 21

portance for the attachment of particle to the fluid in-terface [161]. Safouane et al. [161] compared the shearmoduli of monolayers of fumed silica with different hy-drophobicity degree at the same coverage, finding the in-crease of both the storage and the loss moduli with theparticle hydrophobicity. The behaviour of particles withlow hydrophobicity was found mainly elastic, whereas theincrease of the hydrophobicity leads to a mainly viscousbehaviour with a gel point (G′ = G′′) found for parti-cles with contact angle around 90◦. The effect of the hy-drophobicity on the aforementioned system was extendedby Zang et al. [45, 52, 198]. They found that the storagemodulus does not present any dependence on the strainamplitude for low values of the strain amplitude, with thestorage modulus being almost two orders of magnitudehigher that the lost modulus. The monolayers present amelting transition when the strain amplitude overcomes acertain value (yield stress), with the loss modulus becom-ing maximum and the storage modulus dropping. Whenthe deformation frequency is small a mainly viscous be-haviour was found, becoming mainly elastic for high fre-quencies. The crossover appears for frequencies close tothose in which G′′ is maximum. This behavior is reminis-cent to that observing in 3D soft solids that is the con-sequence of the decrease of the characteristic time of thestructural relaxation due to the increase of the strain-rateamplitude [199]. Similar reminiscence was also found inthe quasi-linear dependence of the relaxation time on theshear rate. An interesting aspect of this monolayer is itsself-healing character upon the stress release. This showsan important dependence on the coverage and wettabilityof the particles, with wettability playing a critical in thecontrol of the yield and melting stresses of particle-ladeninterfaces. Similar behavior to the above discusses werefound independently by Vandebril et al. [200].

Beyond the understanding of the response againstshear of the formed layers, the study of the evolution of therheological properties during the formation of the layerspresent certain interest [201]. The study of the adsorp-tion kinetics of silver nanoparticles (10–50 nm of diam-eter) at the water/toluene interface by rheological mea-surements evidences the increase of G′ and G′′ with time.This is compatible with a densification during the equili-bration process of the layer. The equilibrium films presenta mainly elastic behavior and the negative slope foundfor the dependence of G′′ on the deformation frequencyevidence the 2D glassy nature of the adsorbed layers. Fur-thermore, a significant dependence of the response on thestrain amplitude was found in this system. Using strainsweep measurements shear thickening phenomena in G′′

were found at large strain amplitudes, whereas no de-pendence of G′ on the strain amplitude were found untilthe shear thickening point. This shear thickening is de-scribed by a power law with relation 2:1 on the exponentsof the storage and loss moduli. For gold nanoparticles atthe water/vapor interface a rather different behavior wasreported [36,37,202,203]. The shear response of the abovementioned system presents a gel-like behavior character-ized by a strain induced softening. Furthermore, the rhe-ological response was independent of the applied strain

Fig. 7. Experimental (lines) and calculated (symbols) depen-dences of the interfacial shear stress σ on the amplitude ofstrain γ at a constant frequency ω = 0.628 rad s−1 for silicananoparticles decorated with CTAB, using different concen-trations of surfactant Cs (expressed in mM). Reproduced fromref. [202] with permission from The Royal Society of Chemistry.Copyright (2017).

until a threshold value close to 0.1%. Once the strain over-comes the aforementioned threshold the storage modulusdrops. The dependence of the viscoelastic moduli on theinterfacial coverage for this system can be described interms of a power law with an exponent assuming a valuearound 0.65, which is reminiscent of a percolating sys-tem [158,204,205].

Minor attention has been paid so far to the shear re-sponse of mixtures of particles and surfactants at fluidinterfaces. Maestro et al. [199] explored the effect of thesurfactant concentration on the shear rheology of silicananoparticle-laden interfaces. Strain-sweep experimentsshown in fig. 7 revealed that silica nanoparticles trappedat air-water interface form a 2D solid state with amor-phous order. Further, they proposed a theoretical modelto describe how this solid-like state deforms under a shearstrain ramp up to and beyond a yielding point whichleads to plastic flow [200]. The model accounts for all theparticle-level and many-body physics of the system: non-affine displacements, local connectivity, and its evolutionin terms of cage-breaking, and inter-particle interactionsmediated by the particle chemistry and colloidal forces. Inaddition, the yielding behavior of surfactant-decorated sil-ica nanoparticles has also been studied by large-amplitudeoscillatory rheology [201].

The interfacial interaction of lipids and silica with dif-ferent degrees of hydrophobicity was analyzed by Mass etal. [206]. They found two-step adsorption kinetics at thewater/oil interface. The first step appears in time-scalearound 1 hour. During this step G′ increases due to the

Page 14 of 21 Eur. Phys. J. E (2018) 41: 97

formation of an elastic layer presenting high cohesion. Thesecond step is much slower and characterized by a slow in-crease of both G′ and G′′ due to the accumulation of mate-rial at the interface. This continues until the steady stateis reached. The values of the storage and loss moduli ofthe layers are several orders or magnitude above those ex-pected for pure surfactant monolayers in agreement withother studied [161,207,208].

8 Active particles at fluid interfaces

In general, active colloids use as external input for theirautonomous motion energy obtained from the environ-ment [209–221]. There are several propulsion mechanismsfor these materials, among them chemical reactions andexternal fields are probably the most extended [220]. Manyof that is known about active particles in relation to theirbulk behavior. However, the understanding of the effectof its confinement at interfaces presents particular inter-est because the restrictions associated with the reduceddimensionality can drive significant differences on theirautonomous motion [220]. In the following some aspectsof the interfacial behavior of active colloids trapped atfluid interfaces will be discussed.

The main difference associated with the attachment ofparticle to fluid interface is that the interface constrainsthe particle motion to 2D. Thus, the motion of particlesin the direction perpendicular to the interface is forbid-den, and the motion along the interface leads to dragforces similar to those appearing for the particles in thebulk [222]. When water/vapor interfaces are considered,the vapor phase presents an important role on the con-finement effects because it induces an almost negligiblestress tangent to the interface. This is similar to that hap-pening for active particles moving in an unbounded fluidpresenting a plane of mirror symmetry which enables forthe application of similar propulsion mechanisms for theactive particles at the interface than in the bulk [223–225].

Another important aspect is associated with the hy-drodynamic flows that accompany the particles. Theseare strongly dependent on the proximity of particles tothe fluid boundaries. They enable the hydrodynamic cou-pling between translation and rotational motions whichallow particles to move linearly due to the action oftorques associated with external fields, e.g. electric ormagnetic [221,226]. These torques lead to a rolling motionof the particles along the fluid interface describing the so-called colloidal moonwalk [221]. In general, the motion ofactive particles at fluid interface occurs with the particlesrotating toward the viscous fluid [227].

The role of capillary forces on the motion of parti-cles attached to fluid interfaces is essential, constrainingfurtherly the rotation of particles. For self-phoretic col-loids, capillary forces enhance almost one order or mag-nitude the persistence length of their swimming motion.This is associated with a reduction of the rotational dif-fusion due to the enhanced drag mediated by thermallyactivate fluctuations of the contact line [228, 229]. Fur-thermore, capillary forces also limit the rotation of par-ticles around the two axes parallel to the interface, thus

the motion is strongly correlated to the initial orientationof particle which is correlate to the surface properties ofparticles [230].

The motion of active particles at fluid interfaces canbe modulated by the surface tension and the parame-ter allowing its modification, e.g. temperature or surfac-tant concentration. This enables for the motion of a par-ticular types of active particles, the so-called Marangonisurfers [231,232]. Marangoni surfers use energy originatedby chemical reactions or external energy inputs to in-duce surface tension gradient at the interface. This leadsto forces and torques that provide the bases for a highspeed motion of particles to regions of high surface ten-sion. Thus, particle motion is accompanied by Marangoniflows that induce interactions between particles and thesystem boundaries [233]. These interactions can be eitherattractive or repulsive, leading to the formation of assem-blies and particle swarms. Further details on the behaviorof active colloids trapped at fluid interfaces can be foundin the work by Fei et al. [220] and references therein.

9 Particles at fluid interfaces on thestabilization of dispersed system

The stabilization and properties of dispersed systems(foams, emulsions and thin films) is considered to beclosely correlated to the interfacial and mechanical prop-erties of single interfaces, especially when particles areused for their stabilization. This is because particle-ladeninterface allows hindering, at least partially, the pro-cesses determining the destabilization of dispersed sys-tems, mainly emulsions and foams, e.g. creaming (or sedi-mentation), flocculation, coalescence, and Ostwald ripen-ing [8, 14, 234–237]. When the stabilization of dispersedsystems is considered, the stability of the liquid filmformed between drops or bubbles is essential. An impor-tant aspect of this stability is related to their mechanicalproperties, the adsorbed film must be able to dampen ex-ternal perturbations in order to avoid the destabilizationof the dispersed systems and its breaking.

Particle are very interesting for the stabilization ofdrops and bubbles, because, as was discussed above,they can remain irreversibly trapped at the fluid inter-face leading to particle-stabilize foams and Ramsdem-Pickering emulsions [42,43,66,238]. Especially interestingare those systems in which drops or bubbles are highlycoveraged. Several authors have confirmed the role ofthis latter aspect on the stabilization of dispersed sys-tems [193,239,240]. Their results showed that beyond theimportance of the mechanical stability of the particle-laden interface, the steric hindrance associated with theformation of a sufficiently dense layer is essential for sta-bilization purposes. Stratford et al. [241] and Maestroet al. [242] showed that jammed particle-laden interfacespresent the highest efficiency on the stabilization of emul-sions and foams, respectively which agrees with the re-sults of the studies of dispersed systems stabilized by sil-ica nanoparticles carried out by Frith et al. [243]. This lat-ter showed that the formation of a close-packed particle

Eur. Phys. J. E (2018) 41: 97 Page 15 of 21

layer is mandatory to confer rigidity to drops or bubbles,favoring the stabilization processes. Jamming of particle-laden interface arrests the interfacial tension driven coars-ening, enhancing the stability of the interfaces. It is worthmentioning that there is no linear correlation between thesolid concentration and the stabilization of dispersed sys-tems. The rheological properties of the particle-laden in-terface are also influenced by the coverage as was abovediscussed. Thus, the viscoelastic properties of the layersplay also an important role on the stabilization of thefoams and emulsions because they control the film thin-ning processes. The importance of the mechanical prop-erties was confirmed in the studies by Sullivan and Kil-patrick [244]. They showed that the stabilization of thedispersed system was enhanced by particles forming rigidand stagnant films. Therefore, it is possible to assumethat the understanding of the inter-particle interactionsis essential for controlling the stabilization of dispersedsystems [245]. This is evidenced because particle bridgingcan lead to a further stabilization of foams and emulsions,especially when the coverage is small. These conditionsallow the direct aggregation of drops or bubbles causingstable flocs. These interfaces in close contact can lead tothe formation of long regions of particle bridges, the so-called particle zips. This leads to the formation of net-worked monolayers that provide additional stabilizationto the dispersed systems [240,246].

From the above picture, it is clear that the presence ofparticles attached to fluid interfaces is essential to preventdrops and bubbles coalescence, enabling the stabilizationof emulsions and foams. It is worth mentioning that themorphology and droplet size distribution is governed bydimension and contact angle of particles at the fluid inter-face. The stabilization requires a partial wettability of theparticles by both phases. Considering particles at an arbi-trary fluid interface, two different situations can appear.For relatively hydrophilic particles (θ < 90◦) the forma-tion of oil(air)/water dispersions is preferred for mixturescontaining equal volumes of both fluid phase. The oppo-site is true for hydrophobic particles (θ > 90◦). Thus,θ = 90◦ must be considered as an inversion point whichis defined by the equal affinity of the particles for bothfluid phases [238]. It is worth mentioning that the stabil-ity of foams and emulsions can be controlled by the addi-tion of surfactants that can favor the ability of particlesto reside at the fluid interface [247]. This is understoodclearly from the results by Binks et al. [248]. They foundthat for emulsions stabilized by silica nanoparticles and abicatenary cationic surfactant the concentration of surfac-tant allows tuning the transition between different typesof emulsions as a consequence of the hydrophobization de-gree of the nanoparticles. The study of this phenomenonwas extended by measurements of the contact angle ofparticles at the fluid interface as function of the surfac-tant concentration, and they found that, for low surfactantconcentrations, particles remain hydrophilic with contactangle lower than 90◦ stabilizing oil in water (o/w) emul-sions, whereas for intermediate surfactant concentrationsthe particles become hydrophobic (θ > 90◦) and water inoil emulsions (w/o) were favored. For the highest surfac-

tant concentration, a rehydrophilization of the particlesoccurs and the contact angle drops to values lower than90◦ and the emulsions becomes o/w again [249]. Similareffects have been reported using particles chemically mod-ified to present different degrees of hydrophobicity [250].The effect of the changes of particle wettability can be alsoused for foam stabilization [251–253]. However, no studiesof the transition from aqueous foams to structures formedby free aqueous drops surrounded by a particle shell usingsurfactant to tune the hydrophilicity of the particles arepresent in the literature. However, these latter structures,dry water or liquid marbles, have been obtained using hy-drophobic particles [254,255].

It is also important to consider the role of the menisciformed by the contact line. Different studies have pointedout that the non-uniform wetting of the particles can af-fect the energetic landscape and the ability of particles tostabilize dispersed systems [80, 97, 196]. Ally et al. [256]demonstrate that the adhesion of particles to fluid in-terfaces depends on the particle wettability and edge ge-ometry, which is important for controlling the behaviorof particle-laden interface. Furthermore, the role of themenisci deformation due to gravitational effects for par-ticles bigger enough cannot be neglected as a potentialsource of destabilization [257].

The effectiveness of colloidal particles in stabilisingemulsions and foams depends in part on the formation ofa sufficiently dense layer of particles at the interface. Therheological properties of the interfacial layers also changeas the concentration of particles at the interface increasesand complete surface coverage is achieved. For high par-ticle concentration the interfaces exhibit viscoelastic be-haviour. The viscous properties govern rheological prop-erties at low concentrations, while the elastic propertiesare dominant at high particle concentrations. The elasticcontribution to the viscoelastic behaviour is largely dueto the inter-particle interaction between particles. Theseinteractions become significant at sufficiently high parti-cle concentration. The viscoelastic nature of the interfacesaffects the stability by decreasing the rate of film thinningbetween coalescing droplets.

It was mentioned above that the mechanical behaviourof interfaces, both shear and dilational, plays an essentialrole for controlling the interfacial stability and the defor-mation properties of coated drops and bubbles. It can beexpected that the destabilization by drainage can be par-tially prevented by the increase of the shear viscosity andthe dilational modulus [194]. Several authors have tried todeepen on the correlations existing between the interfacialproperties of particle-laden interfaces and the stabiliza-tion of dispersed systems [53,66,242,258,259]. Cervantes-Martınez et al. [258] proposed that particle-laden inter-faces presenting high resistance to the compression allowsone to increase the stability of foams due to the decreaseof the shrinking of small bubbles. They used the Gibbs cri-terion to establish the conditions for the stabilization ofdispersed systems on the basis of the relationship betweenthe surface tension and the dilational elasticity. Accordingto the Gibbs criterion, only those particle-laden interfacesverifying that E > γ/2, with E being the elastic modulus,

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can be stable. Stocco et al. [53] extended the applicationof the Gibbs criterion to the description of the stabiliza-tion of emulsions. However, their results pointed out thatsuch approach is only valid when emulsions or foams areformed by spherical drops or bubbles. Furthermore, thestudies by Stocco et al. [53] showed that gel-like inter-faces present the better capacities to stability dispersedsystems in agreement with the above discussed effect ofthe interfacial jamming. However, recent works have con-tributed to the controversy about the correlations exist-ing between the rheological properties and the stabiliza-tion of dispersed systems. Santini et al. [79, 110, 112, 260]showed that the use of carbon particles allows one tostabilize foams and emulsion, even though they do notfound any correlation between the stability of the dis-persed systems and their rheological properties. This con-troversy is also feed by the studies of the stabilizationof foam and emulsions by mixtures of silica nanoparticlesand palmitic acid [111,258]. Silica nanoparticles decoratedwith palmitic acid do not allow foam stabilization, eventhough the dilational viscoelastic modulus present relativehigh values (> 100mN/m) [53]. However, the stabilizationof emulsions at the water/hexane interface was possiblewith a poor dependence of the emulsion stability on therheological properties [111].

The above discussion concerns so far to the role ofthe dilational modulus on the stabilization of dispersedsystems. However, the influence of the shear modulus isclearly due to its close correlation to the interfacial struc-ture and coverage. Several authors have shown that theformation of gel-like layers is essential for a good sta-bilization of the dispersed systems [190, 200, 261]. Thiswas confirmed by Brugger et al. [262] using poly(N-isopropylacrylamide) particles for the stabilization ofemulsions, pointing out that high values of G′ providesgood conditions for the emulsion stabilization, whereas theopposite is true for high values of G′′.

The ability of particle-laden interface to provide a highstability of foams and emulsions has provided the bases fortheir use as template for the production of porous mate-rials, e.g. solid foams. These materials can be obtained bydrying and sintering the wet system or directly by the so-lidification of the bulk liquid phase [15, 16]. Gonzenbachet al. [253, 263] take advantage of this idea for the sta-bilization of solid foams using liquid foams stabilized bymixtures of particles and different short length surfactantas precursors. Zabiegaj et al. used similar approaches toprepare particle stabilized solid foams with carbonaceousand alumina particles [110,264,265].

10 Conclusions

The interest for understanding the physico-chemical basesgoverning the formation and properties of particle-ladeninterfaces has undergone a significant growth in recentyears due to their implication in several technological andindustrial fields. Despite the noticeable experimental andtheoretical efforts to unravel the complex physics underly-ing the behavior of these systems a comprehensive descrip-

tion is difficult. This is in part due to the many parametersaffecting its behavior: particle size, chemical nature, mor-phology, nature of the interface. On the other side, thisallows controlling the morphology and mechanical proper-ties of the formed layers. This has a big importance in thepreparation of complex and hierarchical systems bases onparticle-laden interfaces. Many experimental efforts havefocused their interest on the understanding the equilib-rium and dynamics properties of adsorbed and spread lay-ers of particles at fluid interfaces. However, there exists alack of theoretical work to correlate the experimental find-ing with accurate models. Thus, the fully understanding ofthe behavior of particle-laden interface requires multidis-ciplinary efforts. This review has tried to present criticallythe state of art of the topic, showing the level of under-standing achieved in recent years in the description of thebehavior of such intriguing systems.

This work was funded by MINECO under grant CTQ-2016-78895-R and carried out in the framework of the COST ActionMP-1305. Authors thank R.G. Rubio, F. Ortega, L. Liggieriand F. Ravera for their support along these years.

Author contribution statement

The three authors has contributed equally in the prepara-tion and discussion of the present review.

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